Asymptotic behavior of dissipative systems / Jack K. Hale

Auteur: Hale, Jack Kenneth (1944-2009) - AuteurType de document: MonographieCollection: Mathematical surveys ; 25Langue: anglaisPays: Etats UnisÉditeur: Providence : American Mathematical Society, 1989Description: 1 vol. (IX-198 p.) ; 26 cm ISBN: 9780821874806 ; rel. Résumé: This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor. (source : AMS).Bibliographie: Bibliogr. p. 187-196. Index. Sujets MSC: 37Lxx Dynamical systems and ergodic theory -- Infinite-dimensional dissipative dynamical systems
35-02 Partial differential equations -- Research exposition (monographs, survey articles)
35Lxx Partial differential equations -- Hyperbolic equations and systems
35B40 Partial differential equations -- Qualitative properties of solutions -- Asymptotic behavior of solutions
En-ligne: Zentralblatt | MathSciNet | AMS
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Bibliogr. p. 187-196. Index

This book is directed at researchers in nonlinear ordinary and partial differential equations and at those who apply these topics to other fields of science. About one third of the book focuses on the existence and properties of the flow on the global attractor for a discrete or continuous dynamical system. The author presents a detailed discussion of abstract properties and examples of asymptotically smooth maps and semigroups. He also covers some of the continuity properties of the global attractor under perturbation, its capacity and Hausdorff dimension, and the stability of the flow on the global attractor under perturbation. The remainder of the book deals with particular equations occurring in applications and especially emphasizes delay equations, reaction-diffusion equations, and the damped wave equations. In each of the examples presented, the author shows how to verify the existence of a global attractor, and, for several examples, he discusses some properties of the flow on the global attractor. (source : AMS)

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